The recently released iOS 10.2 adds a new “Preserve Settings” settings to the Camera app. You can now preserve the last used settings for Camera Mode and Photo Filter. Go to Settings > Photos & Camera > Preserve Settings to turn on the switches.
iOS defaults to opening the Camera in Photo mode. By turning on the Camera Mode in Preserve Settings, the Camera will now open in your last used camera mode. This is useful if you predominately use a particular camera mode.
Similar to Camera Mode, the Photo Filter switch will preserve the last used filter, instead of reset to None when you next use the Camera app.